Test 1 Preparation
Please refer to the following problems as you begin to prepare for Exam 1.
1. Be able to construct truth tables such as those in exercises 1.2.2 and Participation Activity 1.3.5
2. Be able to determine the number of rows a truth table should have such as in Participation Activity 1.2.3
3. Be able to construct a truth table to show a tautology and logical equivalence such as those in Exercise 1.4.1 and 1.4.4
4. Be able to know and apply the definitions of Converse, Inverse, and Contrapositive
5. Be able to use De Morgan's Law to construct a truth table and matching the correct steps such as Participation Activity 1.5.4
6. Be able to fill in the steps for one of the problems in Exercises 1.5.1 and 1.5.2
7. Be able to indicate whether a proposition is true or false like the ones in Exercises 1.6.2 and 1.7.2 and 1.9.3
8. Be able to determine whether an argument is valid or invalid and construct truth tables to support your answer such as in Exercise 1.11.1
9. Be able to fill in the steps of a logical proof such as the ones in Exercise 1.12.1 (The steps will be given, but you have to supply the reasons)
Test 2 Preparation
Please refer to the following problems as you begin to prepare for Exam 2.
1. Be able to write a direct proof such as those in Exercise 2.2.1
2. Be able to write a proof by exhaustion such as those in Exercise 2.1.1
3. Be able to write a proof by contrapositive such as those in Exercise 2.3.1
4. Be able to write a proof by contradiction such as those in Exercise 2.4.1 and similar to Theorem 2.4.1
5. Be able to write a proof by using cases such as those in Exercise 2.5.1
Test 3 Preparation
Please refer to the following problems as you begin to prepare for Exam 3.
1. Be able to determine whether certain items are members of a set such as Participation Activities 3.1.2-3.1.4
2. Be able to write the roster notation and set builder notation such as in Participation Activity 3.1.5 and Exercise 3.1.4
3. Be able to determine the number of elements in a set such as in Participation Activity 3.1.1
4. Be able to determine whether sets are subsets such as in Participation Activity 3.1.8 and Exercises 3.1.1 and 3.1.3
5. Be able to list all the elements of a subset. (ie: given {a,b}, write all the members that form the subset.
6. Be able to determine the elements in a power set and be able to write a power set such as in Participation Activity 3.2.3
and Exercise 3.2.3
7. Be able to find union and intersections such as in Exercise 3.3.1
8. Be able to find the difference between two sets such as in Participation Activity 3.4.1
9. Be able to find complements and use the set identities such as in Participation Activity 3.4.5 and Exercise 3.5.2
10. Be able to find the Cartesian product and its cardinality between two sets such as in Participation Activity 3.6.1 and
Participation Activity 3.6.2 number 5
Test 4 Preparation
Please refer to the following problems as you begin to prepare for Exam 4.
1. Be able to determine whether a function is well-defined such as in Participation Activity 4.1.5
2. Be able to find the domain, codomain, and range of a function and tell whether it is 1-1, onto, or bijective such as in
exercise 4.1.1
3. Be able to prove and/or disprove that a function is injective (consult the internet if need be)
4. Be able to determine whether a function is 1-1, onto, or bijective, and if it is bijective, be able to find its inverse such
as in Participation Activities 4.4.4 and 4.4.5
5. Be able to show that two function are inverses of one another such as the composition function given in the notes where
f(x)=3x-2 and the inverse was y=(x+2)/3
6. Be able to express an exponential function in equivalent terms such as in Participation Activity 4.6.1
7. Be able to determine whether a digraph has walks, circuits, paths, cycles, in-degrees and out-degrees such as in
Participation Activity 6.3.4
8. Be able to perform matrix multiplication (when possible) with any numbers, not just boolean, similar to Participation Activity 6.6.6 only any numbers can be used
Test 5 Preparation
Please refer to the following problems as you begin to prepare for Exam 5.
1. Be able to determine whether a sequence is geometric or arithmetic and find the common difference or common ratio
similar to Participation Activities 8.1.4 and 8.1.6 and Exercise 8.1.2
2. Be able to use the recurrence definition and formula an = a1 + (n-1)d to find the given term of an arithmetic sequence
similar to Exercise 8.2.1
3. Be able to use the change of variable rules to rewrite summations similar to Participation Activity 8.3.4 and Exercise 8.3.4
4. Be able to prove an identity by Mathematical Induction similar to Example 8.4.1 and Exercise 8.4.2
5. Be able to find the recursive definition for a given function similar to Participation Activity 8.7.2
6. Be able to find a characteristic equation for a linear recurrence relation similar to Participation Activity 8.11.2 and 8.11.3
and Exercise 8.11.1
7. Be able to use The Division Algorithm and compute mod n similar to Participation Activity 9.1.3 and Exercise 9.1.1
8. Be able to verify congruence relations similar to Participation Activity 9.2.2 and Exercise 9.2.4
9. Be able to compute arithmetic expressions mod n similar to Participation Activity 9.2.3 and 9.2.4 and Exercise 9.2.1
10. Be able to formulate the addition and multiplication tables for a given ring of integers similar to Exercise 9.2.2 and
perform calculations in that ring similar to Participation Activity 9.2.1
11. Be able to use the Extended Euclidean Algorithm to compute the gcd of two numbers similar to Participation Activity
9.5.1 and 9.5.2 and Exercise 9.5.1
Test 6 Preparation
Please refer to the following problems as you begin to prepare for Exam 6.
1. Be able to use the Sum and Product Rules similar to Exercise 10.1.1
2. Be able to use the Generalized Product Rule similar to Exercise 10.3.1
3. Be able to count permutations such as in Exercises 10.4.2 and 10.4.3
4. Be able to work with subsets (combinations) such as in Exercises 10.5.1 and 10.5.3 and 10.5.7
5. Be able to work with permutations and combinations in various settings similar to Exercise 10.6.1
6. Be able to count permutations with repetitions similar to Exercise 10.8.4
7. Be able to count multisets and assignment of object problems similar to Exercise 10.10.2
8. Be able to use the Inclusion-Exclusion Principle such as in Participation Activities 10.11.4 and 10.11.5
9. Be able to generate permutations and combinations in lexicographic order similar to Exercise 11.1.2
10. Be able to use the Binomial Theorem to find coefficients similar to Exercise 11.2.1
11. Be able to use the Pigeonhole Principle as it applies to sums of intergers similar to Exercise 11.3.4
12. Be able to use generating functions to determine coefficients from a product of polynomials similar to Exercise 11.4.2
Final Exam Preparation
Please refer to Exams 1-6 as you begin to prepare for the Final Exam. Be sure to review all questions on each exam and know how to complete each problem.
Please refer to the following problems as you begin to prepare for Exam 1.
1. Be able to construct truth tables such as those in exercises 1.2.2 and Participation Activity 1.3.5
2. Be able to determine the number of rows a truth table should have such as in Participation Activity 1.2.3
3. Be able to construct a truth table to show a tautology and logical equivalence such as those in Exercise 1.4.1 and 1.4.4
4. Be able to know and apply the definitions of Converse, Inverse, and Contrapositive
5. Be able to use De Morgan's Law to construct a truth table and matching the correct steps such as Participation Activity 1.5.4
6. Be able to fill in the steps for one of the problems in Exercises 1.5.1 and 1.5.2
7. Be able to indicate whether a proposition is true or false like the ones in Exercises 1.6.2 and 1.7.2 and 1.9.3
8. Be able to determine whether an argument is valid or invalid and construct truth tables to support your answer such as in Exercise 1.11.1
9. Be able to fill in the steps of a logical proof such as the ones in Exercise 1.12.1 (The steps will be given, but you have to supply the reasons)
Test 2 Preparation
Please refer to the following problems as you begin to prepare for Exam 2.
1. Be able to write a direct proof such as those in Exercise 2.2.1
2. Be able to write a proof by exhaustion such as those in Exercise 2.1.1
3. Be able to write a proof by contrapositive such as those in Exercise 2.3.1
4. Be able to write a proof by contradiction such as those in Exercise 2.4.1 and similar to Theorem 2.4.1
5. Be able to write a proof by using cases such as those in Exercise 2.5.1
Test 3 Preparation
Please refer to the following problems as you begin to prepare for Exam 3.
1. Be able to determine whether certain items are members of a set such as Participation Activities 3.1.2-3.1.4
2. Be able to write the roster notation and set builder notation such as in Participation Activity 3.1.5 and Exercise 3.1.4
3. Be able to determine the number of elements in a set such as in Participation Activity 3.1.1
4. Be able to determine whether sets are subsets such as in Participation Activity 3.1.8 and Exercises 3.1.1 and 3.1.3
5. Be able to list all the elements of a subset. (ie: given {a,b}, write all the members that form the subset.
6. Be able to determine the elements in a power set and be able to write a power set such as in Participation Activity 3.2.3
and Exercise 3.2.3
7. Be able to find union and intersections such as in Exercise 3.3.1
8. Be able to find the difference between two sets such as in Participation Activity 3.4.1
9. Be able to find complements and use the set identities such as in Participation Activity 3.4.5 and Exercise 3.5.2
10. Be able to find the Cartesian product and its cardinality between two sets such as in Participation Activity 3.6.1 and
Participation Activity 3.6.2 number 5
Test 4 Preparation
Please refer to the following problems as you begin to prepare for Exam 4.
1. Be able to determine whether a function is well-defined such as in Participation Activity 4.1.5
2. Be able to find the domain, codomain, and range of a function and tell whether it is 1-1, onto, or bijective such as in
exercise 4.1.1
3. Be able to prove and/or disprove that a function is injective (consult the internet if need be)
4. Be able to determine whether a function is 1-1, onto, or bijective, and if it is bijective, be able to find its inverse such
as in Participation Activities 4.4.4 and 4.4.5
5. Be able to show that two function are inverses of one another such as the composition function given in the notes where
f(x)=3x-2 and the inverse was y=(x+2)/3
6. Be able to express an exponential function in equivalent terms such as in Participation Activity 4.6.1
7. Be able to determine whether a digraph has walks, circuits, paths, cycles, in-degrees and out-degrees such as in
Participation Activity 6.3.4
8. Be able to perform matrix multiplication (when possible) with any numbers, not just boolean, similar to Participation Activity 6.6.6 only any numbers can be used
Test 5 Preparation
Please refer to the following problems as you begin to prepare for Exam 5.
1. Be able to determine whether a sequence is geometric or arithmetic and find the common difference or common ratio
similar to Participation Activities 8.1.4 and 8.1.6 and Exercise 8.1.2
2. Be able to use the recurrence definition and formula an = a1 + (n-1)d to find the given term of an arithmetic sequence
similar to Exercise 8.2.1
3. Be able to use the change of variable rules to rewrite summations similar to Participation Activity 8.3.4 and Exercise 8.3.4
4. Be able to prove an identity by Mathematical Induction similar to Example 8.4.1 and Exercise 8.4.2
5. Be able to find the recursive definition for a given function similar to Participation Activity 8.7.2
6. Be able to find a characteristic equation for a linear recurrence relation similar to Participation Activity 8.11.2 and 8.11.3
and Exercise 8.11.1
7. Be able to use The Division Algorithm and compute mod n similar to Participation Activity 9.1.3 and Exercise 9.1.1
8. Be able to verify congruence relations similar to Participation Activity 9.2.2 and Exercise 9.2.4
9. Be able to compute arithmetic expressions mod n similar to Participation Activity 9.2.3 and 9.2.4 and Exercise 9.2.1
10. Be able to formulate the addition and multiplication tables for a given ring of integers similar to Exercise 9.2.2 and
perform calculations in that ring similar to Participation Activity 9.2.1
11. Be able to use the Extended Euclidean Algorithm to compute the gcd of two numbers similar to Participation Activity
9.5.1 and 9.5.2 and Exercise 9.5.1
Test 6 Preparation
Please refer to the following problems as you begin to prepare for Exam 6.
1. Be able to use the Sum and Product Rules similar to Exercise 10.1.1
2. Be able to use the Generalized Product Rule similar to Exercise 10.3.1
3. Be able to count permutations such as in Exercises 10.4.2 and 10.4.3
4. Be able to work with subsets (combinations) such as in Exercises 10.5.1 and 10.5.3 and 10.5.7
5. Be able to work with permutations and combinations in various settings similar to Exercise 10.6.1
6. Be able to count permutations with repetitions similar to Exercise 10.8.4
7. Be able to count multisets and assignment of object problems similar to Exercise 10.10.2
8. Be able to use the Inclusion-Exclusion Principle such as in Participation Activities 10.11.4 and 10.11.5
9. Be able to generate permutations and combinations in lexicographic order similar to Exercise 11.1.2
10. Be able to use the Binomial Theorem to find coefficients similar to Exercise 11.2.1
11. Be able to use the Pigeonhole Principle as it applies to sums of intergers similar to Exercise 11.3.4
12. Be able to use generating functions to determine coefficients from a product of polynomials similar to Exercise 11.4.2
Final Exam Preparation
Please refer to Exams 1-6 as you begin to prepare for the Final Exam. Be sure to review all questions on each exam and know how to complete each problem.
